Comparison of two correlated ROC curves at a given specificity or sensitivity level

Stat Med. 2016 Oct 30;35(24):4352-4367. doi: 10.1002/sim.7008. Epub 2016 Jun 20.


The receiver operating characteristic (ROC) curve is the most popular statistical tool for evaluating the discriminatory capability of a given continuous biomarker. The need to compare two correlated ROC curves arises when individuals are measured with two biomarkers, which induces paired and thus correlated measurements. Many researchers have focused on comparing two correlated ROC curves in terms of the area under the curve (AUC), which summarizes the overall performance of the marker. However, particular values of specificity may be of interest. We focus on comparing two correlated ROC curves at a given specificity level. We propose parametric approaches, transformations to normality, and nonparametric kernel-based approaches. Our methods can be straightforwardly extended for inference in terms of ROC-1 (t). This is of particular interest for comparing the accuracy of two correlated biomarkers at a given sensitivity level. Extensions also involve inference for the AUC and accommodating covariates. We evaluate the robustness of our techniques through simulations, compare them with other known approaches, and present a real-data application involving prostate cancer screening. Copyright © 2016 John Wiley & Sons, Ltd.

Keywords: Box-Cox; ROC; correlated biomarkers; delta method; sensitivity; smooth ROC; specificity.

MeSH terms

  • Area Under Curve
  • Biometry
  • Humans
  • Male
  • Prostatic Neoplasms / diagnosis
  • ROC Curve*
  • Sensitivity and Specificity
  • Statistics, Nonparametric*